A Novel Geometric Hierarchical Approach for Dynamic Visual Servoing of Quadrotors

This paper proposes a novel nonlinear geometric hierarchical dynamic visual servoing approach to drive a quadrotor to the desired pose defined by a previously captured image of a planar target. Different from existing works, the key novelty is to extend the position-based nonlinear hierarchical control to image-based nonlinear hierarchical control. More specifically, by seamlessly integrating the nonlinear hierarchical control with the geometric control, and taking full advantage of the cascade property of the system, the proposed visual servoing strategy does not require the thrust force or its derivative to be measurable when compared with the existing backstepping methods, which brings much convenience for practical applications. For the attitude loop, the axis-angle rotation representation is adopted to design a tracking control law on the vector space ${\mathfrak {so}{(3)}}$. In the outer loop, perspective image moments in the virtual image plane are employed as image feedback to construct the outer-loop image-based visual servoing controller with geometric control and backstepping techniques. Based on Lyapunov techniques and the theory of cascade systems, it is rigorously proven that the proposed image-based controller achieves asymptotic stability. Comparative experiments are conducted to show that the proposed approach has advantages of better transient performance, better steady-state performance, and stronger robustness.